Preface ...................................................... xiii
Acknowledgments ................................................ xv
Foreword ..................................................... xvii
1 Basic Concepts ............................................... 3
1.1 Introduction ............................................ 3
1.2 Response Functions and Fluctuations ..................... 4
1.3 Time-Correlation Functions .............................. 6
1.4 Linear Response Theory .................................. 6
1.5 Fluctuation-Dissipation Theorem ......................... 8
1.6 Diffusion, Friction, and Viscosity ...................... 8
1.7 Summary ................................................ 10
2 Phenomenological Description of Relaxation in Liquids ....... 12
2.1 Introduction ........................................... 12
2.2 Langevin Equation ...................................... 13
2.3 Fokker-Planck Equation ................................. 14
2.4 Smoluchowski Equation .................................. 15
2.5 Master Equations ....................................... 16
2.6 The Special Case of Harmonic Potential ................. 16
2.7 Summary ................................................ 17
3 Density and Momentum Relaxation in Liquids .................. 19
3.1 Introduction ........................................... 19
3.2 Hydrodynamics at Large Length Scales ................... 20
3.2.1 Rayleigh-Brillouin Spectrum ...................... 22
3.3 Hydrodynamic Relations between Self-Difrusion
Coefficient and Viscosity .............................. 24
3.4 Slow Dynamics at Large Wave Numbers: de Germes
Narrowing .............................................. 25
3.5 Extended Hydrodynamics: Dynamics at Intermediate
Length Scales .......................................... 27
3.6 Mode-Coupling Theory ................................... 29
3.7 Summary ................................................ 30
4 Relationship between Theory and Experiment .................. 32
4.1 Introduction ........................................... 32
4.2 Dynamic Light Scattering: Probe of Density
Fluctuation at Long Length Scales ...................... 34
4.3 Magnetic Resonance Experiments: Probe of Single-
Particle Dynamics ...................................... 36
4.4 Kerr Relaxation ........................................ 38
4.5 Dielectric Relaxation .................................. 38
4.6 Fluorescence Depolarization ............................ 39
4.7 Solvation Dynamics (Time-Dependent Fluorescence
Stokes Shift) .......................................... 40
4.8 Neutron Scattering: Coherent and Incoherent ............ 41
4.9 Raman Line-Shape Measurements .......................... 43
4.10 Coherent Anti-Stokes Raman Scattering (CARS) ........... 45
4.11 Echo Techniques ........................................ 45
4.12 Ultrafast Chemical Reactions ........................... 47
4.13 Fluorescence Quenching ................................. 47
4.14 Two-Dimensional Infrared (2D-IR) Spectroscopy .......... 48
4.15 Single-Molecule Spectroscopy ........................... 49
4.16 Summary ................................................ 49
5 Orientational and Dielectric Relaxation ..................... 51
5.1 Introduction ........................................... 51
5.2 Equilibrium and Time-Dependent Orientational
Correlation Functions .................................. 55
5.3 Relationship with Experimental Observables ............. 57
5.4 Molecular Hydrodynamic Description of Orientational
Motion ................................................. 57
5.4.1 The Equations of Motion ......................... 58
5.4.2 Limiting Situations ............................. 59
5.5 Markovian Theory of Collective Orientational
Relaxation: Berne Treatment ............................ 59
5.5.1 Generalized Smoluchowski Equation Description ... 60
5.5.2 Solution by Spherical Harmonic Expansion ........ 62
5.5.3 Relaxation of Longitudinal and Transverse
Components ...................................... 64
5.5.4 Molecular Theory of Dielectric Relaxation ....... 64
5.5.5 Hidden Role of Translations Motion in
Orientational Relaxation ........................ 65
5.5.6 Orientational de Gennes Narrowing at
Intermediate Wave Numbers ....................... 66
5.5.7 Reduction to the Continuum Limit ................ 67
5.6 Memory Effects in Orientational Relaxation ............. 68
5.7 Relationship between Macroscopic and Microscopic
Orientational Relaxations .............................. 70
5.8 The Special Case of Orientational Relaxation of Water .. 72
5.9 Lattice Models of Orientational Relaxation ............. 74
5.10 Nonassociated Liquids .................................. 75
5.11 Summary ................................................ 76
6 Solvation Dynamics in Dipolar Liquid ........................ 78
6.1 Introduction ........................................... 78
6.2 Physical Concepts and Measurement ...................... 79
6.2.1 Measuring Ultrafast, Sub-100fs Decay ............. 83
6.3 Phenomenological Theories: Continuum-Model
Descriptions ........................................... 86
6.3.1 Homogeneous Dielectric Models ................... 86
6.3.2 Inhomogeneous Dielectric Models ................. 89
6.3.3 Dynamic Exchange Model .......................... 91
6.4 Experimental Results: A Chronological Overview ......... 93
6.4.1 Discovery of Multiexponential Solvation
Dynamics: Phase-I (1980-1990) ................... 93
6.4.2 Discovery of Subpicosecond Ultrafast Solvation
Dynamics: Phase-II (1990-2000) .................. 94
6.4.3 Solvation Dynamics in Complex Systems: Phase-
Ill (2000-) ..................................... 95
6.5 Microscopic Theories ................................... 97
6.5.1 Molecular Hydrodynamics Description ............. 97
6.5.2 Polarization and Dielectric Relaxation of
Pure Liquid ..................................... 98
6.5.2.1 Effects of Translational Diffusion in
Solvation Dynamics ...................... 98
6.6 Simple Idealized Models ............................... 100
6.6.1 Overdamped Solvation: Brownian Dipolar
Lattice ........................................ 101
6.6.2 Underdamped Solvation: Stockmayer Liquid ....... 102
6.7 Solvation Dynamics in Water, Acetonitrile, and
Methanol Revisited .................................... 102
6.7.1 The Sub-1 OOfs Ultrafast Component:
Microscopic Origin .............................. 104
6.8 Effects of Solvation on Chemical Processes in the
Solution Phase ........................................ 106
6.8.1 Limiting Ionic Conductivity of Electrolyte
Solutions: Control of a Slow Phenomenon by
Ultrafast Dynamics ............................. 107
6.8.2 Effects of Ultrafast Solvation in Electron-
Transfer Reactions ............................. 107
6.8.3 Nonequilibrium Solvation Effects in Chemical
Reactions ...................................... 107
6.8.3.1 Strong Solvent Forces ................. 109
6.8.3.2 Weak Solvent Forces ................... 110
6.9 Solvation Dynamics in Several Related Systems ......... 111
6.9.1 Solvation in Aqueous Electrolyte Solutions ..... 111
6.9.2 Dynamics of Electron Solvation ................. 111
6.9.3 Solvation Dynamics in Supercritical Fluids ..... 112
6.9.4 Nonpolar Solvation Dynamics .................... 112
6.10 Computer Simulation Studies: Simple and Complex
Systems ............................................... 113
6.10.1 Aqueous Micelles ............................... 114
6.10.2 Water Pool in Reverse Micelles ................. 114
6.10.3 Protein Hydration Layer ........................ 114
6.10.4 DNA Groove Hydration Layer ..................... 115
6.11 Summary .............................................. 115
7 Activated Barrier-Crossing Dynamics in Liquids ............. 117
7.1 Introduction .......................................... 117
7.2 Microscopic aspects ................................... 119
7.2.1 Stochastic Models: Understanding from
Eigenvalue Analysis ............................ 119
7.2.2 Validity of a Rate-Law Description: Role of
Macroscopic Fluctuations ....................... 122
7.2.3 Time-Correlation-Function Approach:
Separation of Transient Behavior from Rate
Law ............................................ 124
7.3 Transition-State Theory ............................... 126
7.4 Frictional Effects on Barrier-Crossing Rate in
Solution: Kramers' Theory ............................. 127
7.4.1 Low-Friction Limit ............................. 129
7.4.2 Limitations of Kramers' Theory ................. 130
7.4.3 Comparison of Kramers' Theory with
Experiments .................................... 131
7.4.4 Comparison of Kramers' Theory with Computer
Simulations .................................... 132
7.5 Memory Effects in Chemical Reactions: Grote-Hynes
Generalization of Kramers' Theory ..................... 132
7.5.1 Frequency Dependence of Friction: General
Aspects ........................................ 138
7.5.1.1 Frequency-Dependent Friction from
Hydrodynamics ......................... 138
7.5.1.2 Frequency-Dependent Friction from
Mode-Coupling Theory .................. 140
7.5.2 Comparison of Grote-Hynes Theory with
Experiments and Computer Simulations ........... 142
7.6 Variational Transition-State Theory ................... 143
7.7 Multidimensional Reaction Surface ..................... 144
7.7.1 Multidimensional Kramers' Theory ................ 145
7.8 Transition Path Sampling .............................. 146
7.9 Quantum Transition-State Theory ....................... 148
7.10 Summary ............................................... 149
Appendix ................................................... 150
8 Barrierless Reactions in Solution .......................... 155
8.1 Introduction .......................................... 155
8.2 Standard Model of Barrierless Reactions ............... 158
8.2.1 Exactly Solvable Models for Photochemical
Reactions ...................................... 159
8.2.1.1 Oster-Nishijima Model ................. 160
8.2.1.2 Staircase Model ....................... 161
8.2.1.3 Pinhole Sink Model .................... 162
8.2.2 Approximate Solutions of Realistic Models ...... 164
8.2.2.1 Delta Function Sink ................... 164
8.2.2.2 Gaussian Sink ......................... 165
8.3 Inertial Effects in Barrierless Reactions: Viscosity
Turnover of Rate ...................................... 166
8.4 Memory Effects in Barrierless Reactions ............... 170
8.5 Unusual Features of Barrierless Chemical Reactions .... 172
8.5.1 Excitation Wavelength Dependence ............... 172
8.5.2 Negative Activation Energy ..................... 172
8.6 Multidimensional Reaction Potential Energy Surface .... 174
8.7 Analysis of Experimental Results ...................... 174
8.7.1 Photoisomerization and Ground-State Potential
Energy Surface ................................. 174
8.7.2 Decay Dynamics of Rhodopsin and Isorhodopsin ... 175
8.7.3 Conflicting Crystal Violet Isomerization
Mechanism ...................................... 177
8.8 Summary ............................................... 177
9 Dynamical Disorder, Geometric Bottlenecks, and Diffusion-
Controlled Bimolecular Reactions ........................... 180
9.1 Introduction .......................................... 180
9.2 Passage through Geometric Botdenecks .................. 181
9.2.1 Diffusion in a Two-Dimensional Periodic
Channel ........................................ 181
9.2.2 Diffusion in a Random Lorentz Gas .............. 183
9.3 Dynamical Disorder .................................... 184
9.4 Diffusion over a Rugged Energy Landscape .............. 186
9.5 Diffusion-Controlled Bimolecular Reactions ............ 190
9.6 Summary ............................................... 193
10 Electron-Transfer Reactions ................................ 195
10.1 Introduction .......................................... 195
10.2 Classification of Electron-Transfer Reactions ......... 196
10.2.1 Classification Based on Ligand Participation ... 196
10.2.2 Classification Based on Interactions between
Reactant and Product Potential Energy
Surfaces ....................................... 196
10.3 Marcus Theory ......................................... 197
10.3.1 Reaction Coordinate (RC) ....................... 198
10.3.2 Free-Energy Surfaces: Force Constant of
Polarization Fluctuation ....................... 200
10.3.3 Derivation of ETR Rate ......................... 203
10.3.4 Experimental Verification of the Marcus
Theory ......................................... 206
10.4 Dynamical Solvent Effects on ETRs (One-Dimensional
Descriptions) ......................................... 208
10.5 Role of Vibrational Modes in Weakening Solvent
Dependence ............................................ 210
10.5.1 Role of Classical Intramolecular Vibrational
Modes: Sumi-Marcus Theory ...................... 210
10.5.2 Role of High-Frequency Vibration Modes ......... 213
10.5.3 Hybrid Model of ETR: Crossover from Solvent
to Vibrational Control ......................... 215
10.6 Theoretical Formulation of Multidimensional Electron
Transfer .............................................. 216
10.7 Effects ofUltrafast Solvation on Electron-Transfer
Reactions ............................................. 220
10.7.1 Absence of Significant Dynamic Solvent
Effects on ETR in Water, Acetonitrile, and
Methanol ....................................... 220
10.8 Summary ............................................... 221
Appendix ................................................... 222
11 Forster (or, Fluorescence) Resonance Energy Transfer
(FRET) ..................................................... 226
11.1 Introduction .......................................... 226
11.2 A Brief Historical Perspective ........................ 229
11.3 Derivation of Förster Expression ..................... 230
11.3.1 Expressions for Emission (or fluoriscence)
Spectrum ....................................... 234
11.3.2 Absorption Spectrum ............................ 237
11.3.3 The Final Forster Expression ................... 238
11.4 Applications of Forster Theory to Chemistry,
Biology, and Materials Science ........................ 239
11.4.1 FRET-Based Glucose Sensor ...................... 239
11.4.2 FRET and Macromolecular Dynamics ............... 239
11.4.3 FRET and Single-Molecule Spectroscopy .......... 243
11.4.4 Beyond Organic Dyes as Donor-Acceptor Pairs .... 247
11.4.5 FRET and Conjugated Polymers ................... 249
11.5 Beyond Forster Formalism .............................. 252
11.5.1 Orientation Factor ............................. 252
11.5.2 Point-Dipole Approximation ..................... 253
11.5.3 Contribution of Optically Dark States .......... 254
11.6 Summary ............................................... 257
12 Vibrational-Energy Relaxation .............................. 259
12.1 Introduction .......................................... 259
12.2 Isolated Binary Collision (IBC) Model ................. 261
12.3 Landau-Teller Expression: The Classical Limit ......... 263
12.4 Weak-Coupling Model: Time-Correlation-Function
Representation of Transition Probability .............. 265
12.5 Vibrational Relaxation at High Frequency: Quantum
Effects ............................................... 268
12.6 Experimental Studies of Vibrational-Energy
Relaxation ............................................ 271
12.7 Computer-Simulation Studies of Vibrational-Energy
Relaxation ............................................ 272
12.7.1 Vibrational-Energy Relaxation of Water ......... 272
12.7.2 Vibrational-Energy Relaxation in Liquid
Oxygen and Nitrogen ............................ 274
12.8 Quantum Interference Effects on Vibrational-Energy
Relaxation in a Three-Level System: Breakdown of the
Rate Equation Description ............................. 275
12.9 Vibrational Life Time Dynamics in Supercritical
Fluids................................................. 277
12.10 Summary .............................................. 279
13 Vibrational-Phase Relaxation ............................... 280
13.1 Introduction .......................................... 280
13.2 Kubo-Oxtoby Theory of Vibrational Line Shapes ......... 282
13.3 Homogeneous vs. Inhomogeneous Linewidths .............. 287
13.4 Relative Role of the Attractive and Repulsive Forces .. 289
13.5 Vibration-Rotation Coupling ........................... 289
13.6 Experimental Results of Vibrational-Phase Relaxation .. 290
13.6.1 Semiquantitative Aspects of Dephasing Rates
in Solution .................................... 291
13.6.2 Subquadratic Quantum Number Dependence ......... 291
13.7 Vibrational Dephasing Near the Gas-Liquid Critical
Point ................................................. 292
13.8 Multidimensional IR Spectroscopy ...................... 292
13.9 Summary ............................................... 294
14 Epilogue ................................................... 296
Index ......................................................... 298
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